科学研究

Haitian Xie is an Assistant Professor at Guanghua School of Management, Peking University. He earned his PhD in Economics from UC San Diego in 2023 and his BA in Economics and Mathematics from Wuhan University in 2017. His research interests include causal inference, policy learning, and econometrics. He has published in top economic journals such as Journal of Business & Economic Statistics (single-authored), Journal of Econometrics (single-authored), Theoretical Economics, among others. He is a recipient of the NSFC Young Scientists Fund.

This paper examines policy learning for continuous treatments under unconfoundedness. The continuous-treatment scenario presents greater challenges than the discrete case because welfare estimation becomes a nonparametric issue, even with a known propensity score. This leads to the interaction between two nonparametric stages in policy learning: welfare estimation and policy design, and their respective tuning parameters. Specifically, the bandwidth for welfare estimation must be selected simultaneously with the sieve index for policy space approximation. We contribute by considering two types of policy estimators: semi- and fully data driven. In the semi-data-driven approach, we manually set the relationship between the bandwidth and the order of the sieve policy class and optimize the choice of the sieve class through structural risk minimization. This relationship is determined adaptively based on data using the fully data-driven approach. For both methods, we derive oracle inequalities for the welfare of the procedures. All these procedures can be implemented using the double robustness method. Additionally, we identify other issues unique to the continuous treatment case, such as the theoretical properties of different penalization methods that were not prominent in the discrete case.